01 - Preheat oven to 320°F. Pat lamb shanks dry with paper towels and season generously on all sides with salt and freshly ground black pepper.
02 - Heat olive oil in a large Dutch oven over medium-high heat. Sear lamb shanks on all sides until deeply browned, approximately 8 minutes total. Transfer to a plate.
03 - In the same pot, add sliced onions, carrots, and celery. Cook for 5-7 minutes until softened, stirring occasionally. Add minced garlic and cook for 1 minute more.
04 - Stir in tomato paste and cook for 1 minute. Pour in dry red wine, scraping up browned bits from the bottom of the pot. Simmer for 2-3 minutes.
05 - Add beef stock, fresh rosemary sprigs, dried thyme, and bay leaves to the pot. Return lamb shanks, nestling them into the vegetables. Bring to a gentle simmer.
06 - Cover Dutch oven and transfer to preheated 320°F oven. Braise for 3 to 3.5 hours until meat is very tender and nearly falling from the bone.
07 - Remove lamb shanks to a warm serving platter and tent with foil. Discard bay leaves and rosemary stems from the braising liquid.
08 - Skim excess fat from the surface of the sauce. For thicker consistency, mix cornstarch with 2 tablespoons cold water to form a slurry, then whisk into simmering sauce until thickened.
09 - Taste gravy and adjust seasoning with salt and pepper as needed. Serve lamb shanks with abundant rosemary gravy spooned over the top.